Estimation of Information Theoretic Measures for Continuous Random Variables

By Fernando Perez-Cruz. 2008

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Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, methodology): “Wang et al. (2009b) 1 and Pérez-Cruz (2008) 2 provided an estimator for kl -divergence, and Póczos and Schneider (2011) developed nonparametric methods for the Rényi and Tsallis divergence estimation.”
Revisiting Classifier Two-Sample Tests (2016, methodology): “The reduction of two-sample testing to binary classification was introduced in (Friedman, 2003), studied within the context of information theory in (Pérez-Cruz, 2009; Reid & Williamson, 2011), discussed in (Fukumizu et al.”
Quantifying causal influences (2012, methodology): “modiﬁed structural equation are now given by XS B :=(I −AS¯) −1 ·X B+E +AS ·X′B . To estimate the relative entropy distance between P and PS (with samples XA and XS B), we use the method described in [16]: Let di be the euclidean distance from the ith column in XA to the rth nearest neighbor among t”
Demystifying fixed k-nearest neighbor information estimators (2016, methodology): “For fixed k-NN methods, apart from the works referred to in the main text, detailed experimental comparisons are in [43] and local Gaussian approaches studied in [16, 17, 33] bringing together local likelihood density estimation methods [31, 19] with k-NN driven choices of kernel bandwidth.”
Parametric Bayesian Estimation of Differential Entropy and Relative Entropy (2010, background): “Peréz-Cruz has contributed additional convergence analysis for these estimators [19].”